Compound Interest

…‘tis the stone that will turn all your lead into gold. Remember that money is of a prolific generating nature. Money can beget money, and its offspring can beget more.
Benjamin Franklin

Compound Interest is a commonly used Mental Model which denotes the exponential growth of a resource.

It is the ”addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.1

A=P(1+rn)nt A = P(1+\frac{r}{n})^{nt}
  • $A =$ final amount
  • $P =$ initial principal balance
  • $r =$ interest rate
  • $n =$ number of times interest applied per time period
  • $t =$ number of time periods elapsed

If we deposit $5,000 into a savings account with an annual interest rate of 5%, compounding monthly, the value of the investment after 10 years is as follows.

$P = 500$
$r = 5/100=0.05$
$n = 12$
$t = 10$

A=5000(1+0.0512)1210=8235.0475 A = 5000 (1+\frac{0.05}{12})^{12 * 10} = 8235.0475

There’s also a simpler formula which assumes that interest is compounded once per period, rather than multiple times per period:

A=P(1+r)t A = P(1+r)^t